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Beliebt Rechnen >

derivative of-5x(2x-3^4)

Lösung

\frac{d}{d x} (- 5 x (2 x - 3)^{4})

Lösung

- 5 ((2 x - 3)^{4} + 8 x (2 x - 3)^{3})

Schritte zur Lösung

\frac{d}{d x} (- 5 x (2 x - 3)^{4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d x} (x (2 x - 3)^{4})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (2 x - 3)^{4}

= - 5 (\frac{d x}{d x} (2 x - 3)^{4} + \frac{d}{d x} ((2 x - 3)^{4}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x - 3)^{4}) = 8 (2 x - 3)^{3}

= - 5 (1 \cdot (2 x - 3)^{4} + 8 (2 x - 3)^{3} x)

Vereinfache

= - 5 ((2 x - 3)^{4} + 8 x (2 x - 3)^{3})

Graph

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